The TESS-Keck Survey XVII: Precise Mass Measurements in a Young, High Multiplicity Transiting Planet System using Radial Velocities and Transit Timing Variations

We present a radial velocity (RV) analysis of TOI-1136, a bright TESS system with six confirmed transiting planets, and a seventh single-transiting planet candidate. All planets in the system are amenable to transmission spectroscopy, making TOI-1136 one of the best targets for intra-system comparison of exoplanet atmospheres. TOI-1136 is young ($\sim$ 700 Myr), and the system exhibits transit timing variations (TTVs). The youth of the system contributes to high stellar variability on the order of 50 m s$^{-1}$, much larger than the likely RV amplitude of any of the transiting exoplanets. Utilizing 359 HIRES and APF RVs collected as a part of the TESS-Keck Survey (TKS), and 51 HARPS-N RVs, we experiment with a joint TTV-RV fit. With seven possible transiting planets, TTVs, more than 400 RVs, and a stellar activity model, we posit that we may be presenting the most complex mass recovery of an exoplanet system in the literature to date. By combining TTVs and RVs, we minimized GP overfitting and retrieved new masses for this system: (m$_{b-g}$ = 3.50$^{+0.8}_{-0.7}$, 6.32$^{+1.1}_{-1.3}$, 8.35$^{+1.8}_{-1.6}$, 6.07$^{+1.09}_{-1.01}$, 9.7$^{+3.9}_{-3.7}$, 5.6$^{+4.1}_{-3.2}$ M$_{\oplus}$). We are unable to significantly detect the mass of the seventh planet candidate in the RVs, but we are able to loosely constrain a possible orbital period near 80 days. Future TESS observations might confirm the existence of a seventh planet in the system, better constrain the masses and orbital properties of the known exoplanets, and generally shine light on this scientifically interesting system.